Where can I find the full original social security application from when they apply for a SS number to when they file for socal security?

You may write to The Social Security Administration and may obtain a copy depending on what years you are looking for,

I don't think people usually "apply" for an SS number. It usually gets assigned to you when you're born. It may not have always been this way, but I believe since the SSN's began, this was always an option. So with that in mind, most likely will be found on their birth certificate. And then usually an SSN is listed on their death certificate. If they came here as a foreigner and were naturalized, then you would look up their naturalization paperwork.

Also, if they were born and died before 1936, they would never have had an SSN. The SSN system was not established until 1936 under FDR.

https://www.familysearch.org/wiki/en/U.S._Social_Security_Records_for_Genealogists
has complete instructions. It will cost you $27. Ancestry.com has some on-line. You can access Ancestry from some public libraries and some Family History Centers.

So when the program first started they sent you a letter in the mail telling them this your SS number That seem like it be impossible at that time, So then would I be able to get the full SS death record and the record of when they apply for their retirement benefit I looking for the full record not the index.

That is not going to help you research your genealogy, nor are you going to be able to research/see the orginial application or anything to do with it......... research for your genealogy is based on birth, marriage, death certs, baptism/burial PRs, census, wills/probate records and other personal effects like letters, photographs, memberships etc